Growth Patterns: From Stable Curved Fronts to Fractal Structures

Abstract

The present lectures intend to review some recent experiments on the properties of patterns obtained in growth processes. This covers a very large range of situations and I will limit myself here to three systems which can be considered as archetypes demonstrating some of the effects at work. The three systems, Saffman Taylor viscous fingering (1–37), dendritic crystal growth (38–50), and diffusion limited aggregation (51–68) have been widely studied and reviews on these three problems can be found respectively in references 3–6, 39–42, and 52–55. Though they are related to still other pattern forming systems these have been chosen here for their (relative) simplicity. All three are close to an ideal problem which is intrinsically mathematical.